Over the last century, a vast body of research has developed around manifolds with lower bounds on curvature. In this talk, I will present results on smooth complete manifolds where the first eigenvalue of the operator \(-\gamma \Delta + \mathrm{Ric}\), for \(\gamma > 0\), is bounded below. Here, \(\mathrm{Ric}\) denotes the lowest eigenvalue of the Ricci tensor. This condition is weaker than a pointwise lower bound on Ricci curvature.
I will explore spectral analogues of classical comparison results; and discuss the relevance of this study in the recent solution of the stable Bernstein problem in \(\mathbb{R}^6\). If time permits, I will conclude with possible future directions and open problems. Based on collaborations with Y. Li, M. Pozzetta, P. Sweeney Jr, and K. Xu.
Manifolds with Ricci bounded below in the spectral sense
03.06.2026 11:30 - 13:00
Organiser:
T. Körber, A. Molchanova, F. Rupp
Location: